I would think the question might be asked in terms of "impressive to whom?"
As a fan who tends to appreciate hitting, with a son being a college hitting coach and who also had a 40 plus game hitting streak in college, whether the streak is all within one season or carries over from one season to the next, anything above 30 games is unique andpretty rare. In my view, it is a huge accomplishment and I am not about to lessen it by suggesting there is something wrong/different or of less meaning if it is done in consecutive games, but interrupted because a season ended. Being interrupted by stints on the DL can, in my view, be distinguished. With all of this said, there is a slightly different physical aspect when the streak overlaps 2 seasons. I am not too sure the mental pressure is different, though and not sure it isn't. Can we imagine what pressure would be on a hitter today if they approached the 56 games of DiMaggio?
My perspective is that all in one season vs carry over when one season ends is like Bowie Kuhn putting an asterisk on Roger Maris and his 61 home runs, but in 162 games. Didn't agree with Bowie.